ANALYSIS OF VARIANCE (ANOVA) PT-II


Graphing Interactions in an ANOVA. 
It is often useful to examine a plot of the means by condition when trying to interpret a significant interaction.

To get plot of means by condition from SPSS

Perform a multifactor ANOVA as described above, but do not click the OK button to perform the analysis.
Click the Plots button.
Define all the plots you want to see.
o To plot a main effect, move the factor to the Horizontal Axis box and click the Add button.
o To plot a two-way interaction, move the first factor to the Horizontal Axis box, move the second factor to the Separate Lines box, and click the Add button.
o To plot a three-way interaction, move the first factor to the Horizontal Axis box, move the second factor to the Separate Lines box, move the third factor to the Separate Plots box, and click the Add button.
Click the Continue button.
Click the OK button.

In addition to the standard ANOVA output, the plots you requested will appear in a section titled Profile Plots.

Post-hoc comparisons for when you have two or more factors.
Graphing the means from a two-way or three-way between-subject ANOVA shows you the basic form of the significant interaction. However, the analyst may also wish to perform post-hoc analyses to determine which means differ from one another. If you want to compare the levels of a single factor to one another, you can follow the post-hoc procedures described in the section on one-way ANOVA.
Comparing the individual cells formed by the combination of two or more factors, however, is slightly more complicated. SPSS does provide options to directly make such comparisons. Fortunately, there is a very easy method that allows one to perform post-hocs comparing all cell means to one another within a between-subjects interaction.

We will work with a specific example to illustrate how to perform this analysis in SPSS. Suppose that you wanted to compare all of the means within a 2x2x3 between-subjects factorial design. The basic idea is to create a new variable that has a different value for each cell in the above design, and then use the post-hoc procedures available in one-way ANOVA to perform your comparisons. The total number of cells in an interaction can be determined by multiplying together the number of levels in each factor composing the interaction. In our example, this would mean that our new variable would need to have 2*2*3=12 different levels, each corresponding to a unique combination of our three IVs.

One way to create this variable would be to use the Recode function described above. However, there is an easier way to do this if your IVs all use numbers to code the different levels. In our example we will assume that the first factor (A) has two levels coded by the values 1 and 2, the second factor (B) has two levels again coded by the values 1 and 2, and that the third factor (C) has three levels coded by the values 1, 2, and 3. In this case, you can use the Compute function to calculate your new variable using the formula:

newcode = (A*100) + (B*10) + C

In this example, newcode would always be a three-digit number. The first digit would be equal to the level on variable A, the second digit would be equal to the level on variable B, while the third digit would be equal to the level on variable C. There are two benefits to using this transformation. First, it can be completed in a single step, whereas assigning the groups manually would take several separate steps. Second, you can directly see the correspondence between the levels of the original factors and the level of the composite variable by looking at the digits of the composite variable. If you actually used the values of 1 through 12 to represent the different cells in your new variable, you would likely need to reference a table to know the relationships between the values of the composite and the values of the original variables. If you ever want to create a composite of a different number of factors (besides 3 factors, like in this example), you follow the same general principle, basically multiplying each factor by decreasing powers of 10, such as the following examples.

newcode = (A*10) + B (for a two-way interaction)
newcode = (A*1000) + (B*100) + (C*10) + D (for a four-way interaction)

Regardless of which procedure you use to create the composite variable, you would perform the post-hoc in SPSS by taking the following steps.

Choose Analyze thengoto General Linear Model thengoto Univariate.
Move the DV to the Dependent Variable box.
Move the composite variable to the Fixed Factor(s) box.
Click the Post-Hoc button.
Move the composite variable to the Post-Hoc Tests for box.
Check the boxes next to the post-hoc tests you want to perform.
Click the Continue button.
Click the OK button.

The post-hoc analyses will be reported in the Multiple Comparisons and Homogenous Subsets sections, as described above under one-way between-subjects ANOVA.